S MandayamECE Dept Rowan University Digital Communications 0909

S. Mandayam/ECE Dept. /Rowan University Digital Communications 0909. 402. 03/0909. 504. 01 Fall 2002 Lecture 3 September 23, 2002 Shreekanth Mandayam ECE Department Rowan University http: //engineering. rowan. edu/~shreek/fall 02/digcomm/

S. Mandayam/ECE Dept. /Rowan University Plan • Discussion: ECOMMS Review QUIZ • Baseband Data Transmission • Recall: Digital Signaling • Orthogonal Vector Representation • Binary and Multilevel Signals • Baud Rate, Bit Rate and Bandwidth • Binary Symmetric Channel • • Joint and Conditional Probabilities Baye’s Theorem BER Optimum Receiver • Lab Project 1

S. Mandayam/ECE Dept. /Rowan University Sampling Quantization Source Encoder ADC Data Encryption Encoder Error Control Encoder Channel/ Line Encoder Modulator Analog i/p CODEC MODEM Audio Amp Reconstruction/ DAC Source Decoder Data Encryption Decoder Error Control Decoder DEMUX Analog o/p Equalization / Decision Circuits Demodulator Multiple access channel Antialiasing Filter MUX Digital Communications Transceiver

S. Mandayam/ECE Dept. /Rowan University Waveform Synthesis using Orthogonal Functions Function Generator 1 Function Generator 2 W 1 W 2 S Clock Function Generator N WN w(t)

S. Mandayam/ECE Dept. /Rowan University Vector Representation of a 3 -bit Binary Signal s(t) p(t) Digital signal 5 V 5 V T T t T 0=3 T 5 V Bit shape pulse t p 1(t) Orthogonal set j 3 t 5 V p 2(t) s t p 3(t) 5 V 0 T 2 T Signal vector 3 T t j 2 j 1

S. Mandayam/ECE Dept. /Rowan University Multilevel Signaling Binary Source Binary signal D symbols/second = R bits/second l-bit DAC 4 T 0 2 0 L=2 l Multilevel Signal D symbols/second = R/l R bits/second Ts Tb -2 -4 0 1 2 3 4 5 6 t (ms) 7 8

S. Mandayam/ECE Dept. /Rowan University Recall Waveforms Deterministic Stochastic Signal (desired) • Probability Noise (undesired)

S. Mandayam/ECE Dept. /Rowan University More Probability • Joint Probability • Probability of events A and B ocurring • Conditional Probability • Probability that A will occur, given that B has occured

S. Mandayam/ECE Dept. /Rowan University Baye’s Theorem

S. Mandayam/ECE Dept. /Rowan University Binary Channel Noise 0/1 Digital Modulation System m 0/m 1 Discrete Memoryless Channel r 0/r 1 Channel Transition Diagram m 0 r 0 m 1 r 1 Digital Demodulation System 0/1

S. Mandayam/ECE Dept. /Rowan University Binary Channel • What can you do? • Cannot change channel - limited by physics/current technology • Objective • Design an optimum receiver by developing a suitable decoding algorithm • How? • Develop a probabilistic model for the channel • Assume that the probability of error is dependent on the message that was sent

S. Mandayam/ECE Dept. /Rowan University Channel Transition Probability Diagram P(m 0 ) m 0 P(r 0 m 0 ) P(r 0 P(r 1 P(m 1 ) m 1 r 0 m 1 ) P(r 1 m 1 ) m ) 0 r 1

S. Mandayam/ECE Dept. /Rowan University Summary